Method for establishing active distribution network planning model considering location and capacity determination of electric vehicle charging station

ABSTRACT

Disclosed is a method for establishing an active distribution network planning model considering location and capacity determination of an electric vehicle charging station. In terms of location and capacity determination of electric vehicle charging stations, a traffic flow of electric vehicles is converted into a charging demand flowing in a traffic network, and an electric vehicle traffic network model is established based on an M/M/s queuing model and a flow capturing location model in the traffic field. A distributed generation (including wind power and photovoltaic) and load model is established, based on a time series method. An energy storage element model in a power distribution network is established based on an idea of equivalent load. A nested planning model is established by taking economy and reliability of a power distribution network and a maximum traffic flow intercepted by the electric vehicle charging stations as objectives.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a Continuation-in-part Application of PCTapplication No. PCT/CN2020/114922 filed on Sep. 12, 2020, which claimsthe benefit of Chinese Patent Application No. 201911161559.1 filed onNov. 22, 2019, the contents of which are hereby incorporated byreference.

FIELD

The present disclosure relates to the field of power grid technologies,and more particular, to a method for establishing an active distributionnetwork planning model considering location and capacity determinationof an electric vehicle charging station.

BACKGROUND

With the access of distributed generation (DG) and electric vehicles(EVs), power planning content of a power distribution network becomesmore complex, and more factors need to be considered in terms of accesscosts and comprehensive benefits. On the one hand, DG output and loaddemands have significantly different time-series characteristics.Reasonable access to an energy storage device can store energy inelectricity troughs and release energy in electricity peaks, so as toachieve the complementation between DG and load demands and reducecomprehensive costs of a planning scheme. On the other hand, access toEV charging stations may lead to charging load, and a location andcapacity determination problem may also affect the stability of thepower distribution network and the convenience of EV travel. Therefore,it is of great significance for an active distribution network toestablish an effective planning model including wind-solar storage andcharging stations.

SUMMARY

In view of this, an objective of the present disclosure is to provide amethod for establishing an active distribution network planning modelconsidering location and capacity determination of an electric vehiclecharging station, which can consider mutual influences between a powernetwork and a traffic network at the same time, and make distributionnetwork planning results more suitable to the energy development trendunder a new situation on the premise of satisfying multi-load demands.

The present disclosure is implemented using the following solution: amethod for establishing an active distribution network planning modelconsidering location and capacity determination of an electric vehiclecharging station is provided, including the following steps:

step S1: establishing a traffic network, and establishing, based on anM/M/s queuing model and a flow capturing location model, a trafficnetwork including an electric vehicle charging station;

step S2: establishing an active distribution network model, andestablishing a distributed generation and load time-series model basedon a time-series method; and establishing an energy storage model basedon an equivalent load principle; and

step S3: converting a traffic flow of electric vehicles into anequivalent load of an equivalent charging station, coupling the trafficnetwork with a power grid, and establishing an active distributionnetwork nested planning model considering the traffic network.

Further, step S1 particularly includes:

step S11: calculating an EV charging capacity demand;

calculating an EV charging capacity demand;

calculating a battery pack quantity demand;

$\begin{matrix}{N_{B} = {\sum\limits_{i = 1}^{5}\left( {N_{EVi}\frac{L_{di}}{L_{0i}}a_{i}b_{i}K_{EVdi}} \right)}} & (1)\end{matrix}$

in the formula: N_(B) is a daily demand for battery packs; N_(EVi) is astock of an i^(th)-type EV; L_(di) and L_(0i) are respectively anaverage daily mileage of the i^(th)-type EV and a distance at which thei^(th)-type EV travels on a full charge; and a_(i), b_(i), and K_(EVdi)are respectively attendance rates, a battery replacement ratio, and thenumber of battery packs per vehicle for the i^(th)-type EV;

the charging capacity demand is:

W _(B) =N _(B) P _(C) ^(t) _(charge)/(η_(tran)η_(charge))  (2)

in the formula: η_(tran) is transformer efficiency; η_(charge) ischarger efficiency; P_(c) denotes an average charge power; andt_(charge) denotes a charging time;

step S12: establishing a charging station location and capacitydetermination model;

calculating a traffic flow F_(CS) annually intercepted by a system-widecharging station by using a gravity space interaction model incombination with a Floyd algorithm; of which a calculation formula is asfollows: and

calculating a traffic flow intercepted by a single charging stationaccording to the following formulas:

$\begin{matrix}{{f_{k,t}^{road} = {\frac{\omega_{ko}\omega_{kd}}{D_{k}^{1.5}} \cdot \frac{\sigma_{t}}{\sigma_{RH}}}},{k \in \Omega_{od}},{t \in T}} & (3) \\{F_{CS} = {365 \cdot {\sum\limits_{t = 1}^{24}{\sum\limits_{k \in \Omega_{bd}}{f_{k,t}^{road}x_{k}^{load}}}}}} & (4)\end{matrix}$

in the formula (3): f_(k,t) ^(road) denotes a per-unit value of aone-way traffic flow demand of the shortest path k in a period t; ω_(ko)and ω_(kd) are traffic demand weights of a starting point and an endingpoint of the path k respectively, used to indicate busyness degrees oftraffic nodes; D_(k) is a per-unit value of the length of the path k;σ_(t) and σ_(RH) are travel ratios of EV users in a period t and a peakhour h respectively; Ω_(bd) is a set of shortest paths from any startingpoint o to any ending point d in the traffic network and is obtainedaccording to the Floyd algorithm; T is a set of periods; and x_(k)^(load) indicates a binary variable of whether a flow on the path k canbe intercepted by a charging station, if the path k passes through thecharging station, the variable is 1, and otherwise, the variable is 0;

calculating an equivalent charging load according to the traffic flowintercepted by the single charging station in the following calculationmanners:

$\begin{matrix}{{f_{i,t}^{CS} = {\sum\limits_{k \in \Omega_{od}}{f_{k,t}^{road}x_{k,i}^{road}x_{i}^{CS}}}},{i \in \Omega},{t \in T}} & (5) \\{{\lambda_{i}^{RH} = {\max \left\{ {\left. \lambda_{i,t} \middle| \lambda_{i,t} \right. = {{\overset{\sim}{F}}^{CS}{\frac{\sigma_{t}}{\sum\limits_{t \in T}\sigma_{t}} \cdot \frac{f_{i,t}^{CS}}{\sum\limits_{i \in \Omega}f_{i,t}^{CS}}}}} \right\}}},{i \in \Omega}} & (6) \\{{P_{i,t}^{CS} = {p^{CS}\frac{\lambda_{i,t}}{\mu}}},\ {i \in \Omega},{t \in T}} & (7)\end{matrix}$

in the formula (5), f_(i,t) ^(CS) is a traffic flow intercepted by anode i in a period t; x_(k,i) ^(road) is a binary variable of whetherthe path k passes through the node i; x_(i) ^(CS) is a binary variableof whether a charging station is constructed at the node i; Ω is a setof network nodes; λ_(i,t) is the number of electric vehicles arriving atthe charging station located at the node i at time t to receive acharging service; in the formula (6), P_(i,t) ^(CS) is a charge power ofthe node i at the time t; λ_(i) ^(RH) is an average arrival rate ofto-be-charged vehicles at the node i during rush hours, i.e. the numberof EVs arriving at the charging station to receive the charging serviceper unit of time; {tilde over (F)}^(CS) is a total daily chargingfrequency demand of an EV charging station and needs to be calculatedaccording to W_(B) in the formula (2); {tilde over(F)}^(CS)=W_(B)/preset maximum battery pack capacity; W_(B) is acharging capacity; in the formula (7), p^(CS) is a charge power of asingle charging device; and μ is an average service rate of a singledevice, in units of vehicles per hour; and

step S13: transforming, based on the/M/s queuing model, a capacitydetermination problem of a charging station into the following nonlinearinteger planning problems:

$\begin{matrix}{\min \; z_{i}^{CS}} & (8) \\{s.t.\left\{ {\begin{matrix}{W_{i}^{RH} < W^{allowed}} \\{z_{i}^{CS} \geq \frac{\lambda_{i}^{RH}}{\mu}}\end{matrix},{\forall{i \in \Omega}}} \right.} & (9) \\{{W_{i}^{RH} = {P_{i}^{non}\frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{z_{i}^{CS}}\rho_{i}^{RH}}{{{\lambda_{i}^{RH}\left( z_{i}^{CS} \right)}!}\left( {1 - \rho_{i}^{RH}} \right)^{2}}}},{\lambda_{i}^{RH} \neq 0}} & (10) \\{P_{i}^{non} = \left\lbrack {{\sum\limits_{n = 0}^{z_{i}^{CS} - 1}\frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{n}}{n!}} + \frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{z_{i}^{CS}}}{{\left( z_{i}^{CS} \right)!}\left( {1 - \rho_{i}^{RH}} \right)}} \right\rbrack^{- 1}} & (11) \\{\rho_{i}^{RH} = \frac{\lambda_{i}^{RH}}{z_{i}^{CS}\mu}} & (12)\end{matrix}$

in the formulas: z_(i) ^(CS) is the number of charging devicesconfigured for the node i, which is multiplied by p^(CS) to obtain thecapacity of the charging station at node W_(i) ^(RH) and W^(allowed) arean average waiting time for receiving a charging service during rushhours and a threshold thereof respectively; P_(i) ^(non) is theprobability that charging station devices at the node i are all idle;and ρ_(i) ^(RH) is an average device usage rate of the node i duringrush hours.

Further, step S2 particularly includes:

establishing the active distribution network model, and sampling, basedon a time series method, typical output and different types of typicalload curves of distributed generation including wind power andphotovoltaic, to obtain a DG output value P_(DGi)(t) and a load valueP_(Li)(t) of the node i at the time t; and establishing an energystorage model based on an equivalent load principle, an energy storageelement adjusting strategy being as follows:

calculating an equivalent load P_(eqi) and an average equivalent loadP_(avi) of the node i at the time t,

$\begin{matrix}{{P_{eqi}(t)} = {{P_{Li}(t)} - {P_{DGi}(t)}}} & (13) \\{P_{avi} = {\sum\limits_{t = 1}^{24}{{P_{eqi}(t)}/24}}} & (14)\end{matrix}$

in the formulas: P_(Li)(t) and P_(DGi)(t) represent a load value and aDG output value of the node i at the time t; and

the energy storage element adjusting strategy is particularly asfollows:

when P_(eqi)(t)+ΔP₁<<P_(avi), an accumulator is charged, and ΔP₁ is acharge power;

if |P_(eqi)(t)+ΔP₁−P_(avi)|≤δP_(avi) is met, the accumulator is charged;δ represents a fluctuation coefficient of P_(eqi) around a mean valuethereof;

when P_(eqi)(t)−ΔP₂>>P_(avi), the accumulator is discharged, and ΔP₂ isa discharge power; and

if |P_(eqi)(t)−ΔP−P_(avi)|≤δP_(avi) is met, the accumulator isdischarged.

Further, step S3 particularly includes:

an objective function of the nested planning model being:

$\begin{matrix}{\mspace{79mu} {\min \left\{ \begin{matrix}{f_{1} = {{\frac{{r\left( {1 + r} \right)}^{\eta}}{\left( {1 + r} \right)^{\eta} - 1}C^{inv}} + C^{ope}}} \\{{f_{2} = {\sum\limits_{s = 1}^{96}{\sum\limits_{i = 1}^{n}{U_{s,i}^{level}/\left( {96 \cdot n} \right)}}}},{i \in \Omega},{s \in \Omega_{s}}} \\{{f_{3} = {1/\left( {365 \cdot {\sum\limits_{t = 1}^{24}{\sum\limits_{k \in \Omega_{od}}{f_{k,t}^{road}x_{k}^{load}}}}} \right)}},{t \in T}}\end{matrix} \right.}} & (15) \\{C^{inv} = {{p^{DG}\left( {{c_{1}^{PV}{\sum\limits_{j \in \Omega^{PV}}N_{j}}} + {c_{1}^{WG}{\sum\limits_{k \in \Omega^{WG}}N_{j}}}} \right)} + {c^{CS}{\sum\limits_{i \in \Omega}{z_{i}^{CS}x_{i}^{CS}}}} + {\sum\limits_{k \in \Omega^{BS}}{x_{k}^{BS}\left( {{c_{1}^{BS}S_{\max}^{BS}} + {c_{2}^{BS}P_{\max}^{BS}}} \right)}}}} & (16) \\{C^{ope} = {{c_{2}^{PV}{\sum\limits_{s \in \Omega_{s}}{\sum\limits_{j \in \Omega^{PV}}{\Delta \; t_{s}P_{s,j}^{PV}}}}} + {c_{2}^{WG}{\sum\limits_{s \in \Omega_{s}}{\sum\limits_{j \in \Omega^{WG}}{\Delta \; t_{s}P_{s,j}^{WG}}}}} + {\sum\limits_{s \in \Omega_{s}}{{f_{e}(s)}{P_{em}(s)}\Delta \; t_{s}}}}} & (17) \\{\mspace{79mu} {{P_{em}(s)} = {{\sum\limits_{i = 1}^{n}\left( {P_{s,i}^{L} + P_{s,i}^{CS}} \right)} - \left( {{\sum\limits_{j \in \Omega^{PV}}P_{s,j}^{PV}} + {\sum\limits_{j \in \Omega^{WG}}P_{s,j}^{WG}}} \right) + P_{s}^{loss}}}} & (18) \\{\mspace{79mu} {U_{s,i}^{level} = \left\{ \begin{matrix}{\frac{V_{s,i} - 1}{V^{\min} - 1},{V^{\min} < V_{s,i} \leq 1}} \\{\frac{V_{s,i} - 1}{V^{\max} - 1},{1 < V_{s,i} < V^{\max}}} \\{1.0,{{V_{s,i} \geq V^{\max}};{V_{s,i} \leq V^{\min}}}}\end{matrix} \right.}} & (19)\end{matrix}$

in the formulas: f₁ denotes an economic cost, including a constructioncost C^(inv) and an operation cost C^(ope); r is a discount rate; η isan investment life; f₂ denotes a voltage quality index; U_(s,i) ^(level)is a voltage quality evaluation function value of the node i in ascenario s; n is the total number of network nodes; Ω denotes a set ofnodes; Ω_(s) is a set of scenarios; f₃ denotes a traffic networksatisfaction index; Ω_(od) is a set of shortest paths from any startingpoint o to any ending point d in the traffic network; f_(k,t) ^(road)denotes a per-unit value of a one-way traffic flow demand of theshortest path k in a period t; x_(k) ^(load) denotes a binary variableof whether a flow on the path k is intercepted by a charging state; Tisa set of periods; P^(DG) is a DG unit capacity; x_(i) ^(CS) is a binaryvariable of whether a charging station is constructed at the node i; c₁^(PV) and c₁ ^(WG) are investment costs per unit capacity ofphotovoltaic and wind power generation respectively; Ω^(PV) and Ω^(WG)are sets of nodes for mounting photovoltaic and fans; N_(j) is thenumber of DGs of the j^(th) mounting node; c^(cs) is investment cost ofeach charging device; x_(k) ^(BS) is a binary variable of whether a nodek is put into an energy storage device; Ω^(BS) is a set of nodes formounting energy storage; c₁ ^(BS) and c₂ ^(BS) are a unit capacity costand a charge-discharge power cost of the energy storage devicerespectively; S_(max) ^(BS) and P_(max) ^(BS) maximum energy storagecapacity and maximum charge-discharge power respectively; c₂ ^(PV) andc₂ ^(WG) are unit operation costs of photovoltaic and wind powergeneration respectively; Δt_(s) is an annual cumulative operation timeof a distribution network in a scenario s; P_(s,j) ^(PV) and P_(s,j)^(WG) are outputs of the j^(th) PV or WG in the scenario s; f_(e)(s) andP_(em)(s) are electricity price and electric power demands in thescenario s respectively; P_(s,i) ^(L) and P_(s,i) ^(CS) are a load powerand an EV charge power of the node i in the scenario s; P_(s) ^(loss) iselectric energy loss in the scenario s; V_(s,i) is a voltage amplitudeof the node i in the scenario s; and V^(min) and V^(max) are anallowable lower limit and an allowable upper limit of a node voltagerespectively;

constraints of the nested planning model including traffic networkconstraints and power grid constraints, and the traffic networkconstraints being as follows:

$\begin{matrix}\left\{ {\begin{matrix}{W_{i}^{RH} < W^{allowed}} \\{z_{i}^{CS} \geq \frac{\lambda_{i}^{RH}}{\mu}}\end{matrix},{\forall{i \in \Omega}}} \right. & (20) \\{{\sum\limits_{i \in \Omega}x_{i}^{CS}} \leq N^{CS}} & (21) \\{{{\sum\limits_{i \in \Omega}{\sum\limits_{k \in \Omega_{od}}{f_{k,t}^{road}x_{k,i}^{road}x_{i}^{CS}}}} \geq {\sum\limits_{k \in \Omega_{od}}f_{k,t}^{road}}},{\forall{t \in T}}} & (22) \\{{W_{i}^{RH} = {P_{i}^{non}\frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{z_{i}^{CS}}\rho_{i}^{RH}}{{{\lambda_{i}^{RH}\left( z_{i}^{CS} \right)}!}\left( {1 - \rho_{i}^{RH}} \right)^{2}}}},{\lambda_{i}^{RH} \neq 0}} & (23) \\{P_{i}^{non} = \left\lbrack {{\sum\limits_{n = 0}^{z_{i}^{CS} - 1}\frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{n}}{n!}} + \frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{z_{i}^{CS}}}{{\left( z_{i}^{CS} \right)!}\left( {1 - \rho_{i}^{RH}} \right)}} \right\rbrack^{- 1}} & (24) \\{\rho_{i}^{RH} = \frac{\lambda_{i}^{RH}}{z_{i}^{CS}\mu}} & (25)\end{matrix}$

in the formulas: z_(i) ^(CS) is the number of charging devicesconfigured for the node i, which is multiplied by p^(CS) to obtain acharge power of a single charging device at the node i; λ_(i) ^(RH) isan average arrival rate of to-be-charged vehicles at the node i duringrush hours, i.e. the number of road EVs arriving at the charging stationto receive the charging service per unit of time; x_(k,i) ^(road)denotes a binary variable of whether a flow on the path k can beintercepted by a charging station; Ω_(bd) is a set of shortest pathsfrom any starting point o to any ending point din the traffic network;W_(i) ^(RH) and W^(allowed) are an average waiting time for receiving acharging service during rush hours and a threshold thereof respectively;P_(i) ^(non) is the probability that charging station devices at thenode i are all idle; ρ_(i) ^(RH) is an average device usage rate of thenode i during rush hours; N^(CS) is the maximum number of chargingstations to be constructed; and μ is an average service rate of a singledevice;

the power grid constraints being as follows:

power flow constraints of the power distribution network:

$\begin{matrix}\left\{ {{\begin{matrix}{{P_{s,i}^{L} + P_{s,i}^{CS} - P_{s,i}^{DG}} = {V_{s,i}{\sum\limits_{j = 1}^{n}{V_{s,j}\left( {{G_{ij}\cos \; \delta_{s,{ij}}} + {B_{ij}\sin \; \delta_{s,{ij}}}} \right)}}}} \\{{Q_{s,i}^{L} - Q_{s,i}^{DG}} = {V_{s,i}{\sum\limits_{j = 1}^{n}{V_{s,j}\left( {{G_{ij}\sin \; \delta_{s,{ij}}} - {B_{ij}\cos \; \delta_{s,{ij}}}} \right)}}}}\end{matrix}{\forall{s \in \Omega_{s}}}},{i \in \Omega}} \right. & (26)\end{matrix}$

scenario chance constraints:

$\begin{matrix}{{{\Pr \left\{ {{V^{\min} \leq V_{s,i} \leq V^{\max}},{{P_{s,{ij}}} \leq P_{ij}^{\max}}} \right\}} = {\frac{K_{s}}{96} \geq {\gamma {\forall{i \in \Omega}}}}},{\forall{{ij} \in \Omega^{Line}}}} & (27)\end{matrix}$

DG mounting capacity constraints:

$\begin{matrix}\left\{ \begin{matrix}{{0 \leq P_{s,j}^{PV} \leq {\overset{\_}{P}}_{s,j}^{PV}},{\forall{s \in \Omega_{s}}},{j \in \Omega^{PV}}} \\{{0 \leq P_{s,j}^{WG} \leq {\overset{\_}{P}}_{s,j}^{WG}},{\forall{s \in \Omega_{s}}},{j \in \Omega^{WG}}} \\{{\sum\limits_{s \in \Omega_{s}}\left( {P_{s,j}^{PV} + P_{s,j}^{WG}} \right)} \leq {ɛ{\sum\limits_{s \in \Omega_{s}}{\sum\limits_{i = 1}^{n}P_{s,i}^{L}}}}}\end{matrix} \right. & (28)\end{matrix}$

energy storage capacity and charge-discharge power constraints:

$\begin{matrix}\left\{ {\begin{matrix}{{0 \leq S_{k}^{BS} \leq S_{\max}^{BS}},} \\{{0 \leq P_{k}^{BS} \leq P_{\max}^{BS}},}\end{matrix}{\forall{k \in \Omega^{BS}}}} \right. & (29)\end{matrix}$

in the formulas: Q_(s,i) ^(L) is a reactive load of the node i in thescenario s; P_(s,i) ^(DG) and Q_(s,i) ^(DG) are DG active and reactiveoutputs of the node i in the scenario s; V_(s,j) is a voltage amplitudeof a node j in the scenario s; G_(ij) and B_(ij) are real part andimaginary part of network admittances respectively; δ_(s,ij) is avoltage phase angle difference of the nodes i and j in the scenario s;P_(s,ij) and P_(ij) ^(max) are a power flowing through a line ij and apower limit; K_(s) is the number of scenarios meeting chanceconstraints; γ is a confidence coefficient; Ω^(Line) is a set of powerdistribution network lines; P_(s,j) ^(PV) and P_(s,j) ^(WG) are outputupper limits of PV and WG respectively; ε is a maximum penetration rateof DG access; and S_(k) ^(BS) and P_(k) ^(BS) area current devicecapacity and a charge-discharge power of an energy storage node krespectively.

Compared with the prior art, the present disclosure has the followingbeneficial effects:

1. The present disclosure can reduce construction costs of electricvehicle charging stations to the greatest extent and reduce planningcosts of a power distribution network.

2. Voltage stability is one of the planning objectives of the presentdisclosure. Therefore, the present disclosure can reduce a voltagefluctuation degree of the power distribution network to the greatestextent and make voltage distribution of the power distribution networkmore uniform.

3. The present disclosure combines an electric vehicle network into apower network, fully considers influences of electric vehicle chargingon the power distribution network, and formulates an optimal optimizeddispatching strategy of a power grid in combination with the electricvehicle charging, which has very significant practical significance foroptimized dispatching of electric vehicles connected to the powerdistribution network.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an output power diagram of wind power generation according toan embodiment of the present disclosure.

FIG. 2 is an output power diagram of photovoltaic power generationaccording to an embodiment of the present disclosure.

FIG. 3 is a residential load power diagram according to an embodiment ofthe present disclosure.

FIG. 4 is a commercial load power diagram according to an embodiment ofthe present disclosure.

FIG. 5 is an industrial load power diagram according to an embodiment ofthe present disclosure.

FIG. 6 is a topological diagram of a coupling network of a powerdistribution network and a traffic network according to an embodiment ofthe present disclosure.

FIG. 7 is a flowchart of solution to a planning model according to anembodiment of the present disclosure.

FIG. 8 is a diagram of load time-series characteristics before and aftercharging of a 19 EV according to an embodiment of the presentdisclosure.

FIG. 9 is a diagram of load time-series characteristics before and aftercharging of an EV in spring peak hours according to an embodiment of thepresent disclosure.

FIG. 10 is a diagram of node voltage amplitudes before and aftercharging of an EV in spring peak hours according to an embodiment of thepresent disclosure.

DETAILED DESCRIPTION

The present disclosure is further described below with reference to theaccompanying drawings and embodiments.

It should be noted that the following detailed descriptions are allillustrative and are intended to provide further clarification of thisapplication. Unless otherwise specified, all technical and scientificterms used herein have the same meanings as normally understood by aperson of ordinary skill in the art.

It is important to note that the terms used herein are intended only todescribe specific implementations and are not intended to limitexemplary implementations according to this application. As used herein,the singular forms “a”, “an” and “the” are intended to include theplural forms as well, unless the context clearly indicates otherwise. Inaddition, it should also be understood that when the terms “include”and/or “comprise” are used in this specification, they indicate thepresence of features, steps, operations, devices, components and/ortheir combinations.

This embodiment provides a method for establishing an activedistribution network planning model considering location and capacitydetermination of an electric vehicle charging station, which couples apower network to a traffic network, and implements location and capacitydetermination of an electric vehicle charging station by converting atraffic flow of electric vehicles in the traffic network into anelectric load required by electric vehicle charging while consideringdevice elements such as wind-solar storage in the active distributionnetwork.

The method includes the following steps:

Step S1: Establish a traffic network, and establish, based on an M/M/squeuing model and a flow capturing location model in a traffic field, atraffic network including an electric vehicle charging station.

Step S2: Establish an active distribution network model, and establish adistributed generation (including wind power and photovoltaic) and loadtime-series model based on a time-series method; and establish an energystorage model based on an equivalent load principle.

Step S3: Convert a traffic flow of electric vehicles into an equivalentload of an equivalent charging station, couple the traffic network witha power grid, and establish an active distribution network nestedplanning model considering the traffic network.

In this embodiment, a location and capacity determination model includesan MMs queuing model and a flow capturing location model, and step Sparticularly includes the following steps:

Step S11: Calculate an EV charging capacity demand.

Calculate a battery pack quantity demand:

An EV is typically powered by several battery packs, each of whichconsists of a number of cells in series and in paralle^([12]).Therefore, an EV charging demand can be analyzed with such anintermediate variable as a battery pack quantity demand.

According to different uses, EVs can be classified as buses, servicecars, taxis, private cars, and other vehicles (sanitation vehicles,postal vehicles, etc.). The quantity demand of battery packs is mainlyrelated to information such as a stock of EVs, a daily driving distance,an attendance rate, and a battery replacement ratio of each vehiclemodel. Therefore, the quantity demand of battery packs is calculatedherein, as shown in the formula (1).

$\begin{matrix}{N_{B} = {\sum\limits_{i = 1}^{5}\left( {N_{EVi}\frac{L_{di}}{L_{0i}}a_{i}b_{i}K_{EVdi}} \right)}} & (1)\end{matrix}$

in the formula: N_(B) is a daily demand for battery packs; N_(EVi) is astock of an i^(th)-type EV; L_(di) and L_(0i) are respectively anaverage daily mileage of the i^(th)-type EV and a distance at which thei^(t)-type EV travels on a full charge; and a_(i), b_(i), and K_(EVdi)are respectively attendance rates, a battery replacement ratio, and thenumber of battery packs per vehicle for the i^(th)-type EV.

In this embodiment, it is assumed that the EVs adopt unified lithium-ionbattery packs, each consisting of 15 single cells (of which the ratedvoltage is 3.65 V and the rated capacity is 6 A·h) in series. In thisembodiment, it is deemed that a charging process thereof may beapproximately constant power charging, and a charge power P_(C) of asingle battery pack is approximately 1660 W, and a required durationt_(charge) is 2.5 h. On the other hand, an EV charging station isequipped with a large number of charging devices, and a set of devicesconsist of a transformer and several charging mechanisms attached to it.For the convenience of analysis, assuming that the charging stationperforms electricity distribution according to a maximum demand of an EVbattery pack, the charging capacity demand at this time is:

W _(B) =N _(B) P _(C) t _(charge)/(ηtranlηcharge)  (2)

in the formula: η_(tran) is transformer efficiency; η_(charge) chargerefficiency; P_(c) denotes an average charge power; and t_(charge)denotes a charging time.

Step S12: Establish a charging station location and capacitydetermination model.

In the traffic network, the charging station needs to cover a trafficflow in the network, and the location problem usually needs to considerintercepting as much flow as possible. In this embodiment, a trafficflow F_(CS) annually intercepted by a system-wide charging station iscalculated by using a gravity space interaction model in combinationwith a Floyd algorithm. A calculation formula thereof is as follows:

Calculate a traffic flow intercepted by a single charging stationaccording to the following formulas:

$\begin{matrix}{{f_{k,t}^{road} = {\frac{\omega_{ko}\omega_{kd}}{D_{k}^{1.5}} \cdot \frac{\sigma_{t}}{\sigma_{RH}}}},{k \in \Omega_{od}},{t \in T}} & (3) \\{F_{CS} = {365 \cdot {\sum\limits_{t = 1}^{24}{\sum\limits_{k \in \Omega_{od}}{f_{k,t}^{road}x_{k}^{load}}}}}} & (4)\end{matrix}$

in the formula (3): f_(k,t) ^(road) denotes a per-unit value of aone-way traffic flow demand of the shortest path k in a period t; ω_(ko)and ω_(kd) are traffic demand weights of a starting point and an endingpoint of the path k respectively, used to indicate busyness degrees oftraffic nodes; D_(k) is a per-unit value of the length of the path k;σ_(t) and σ_(RH) are travel ratios of EV users in a period t and a peakhour h respectively; Ω_(od) is a set of shortest paths (OD paths) fromany starting point o to any ending point din the traffic network and isobtained according to the Floyd algorithm; T is a set of periods; andx_(k) ^(load) indicates a binary variable of whether a flow on the pathk can be intercepted by a charging station, if the path k passes throughthe charging station, the variable is 1, and otherwise, the variable is0.

The traffic flow intercepted by the system throughout the year can beused as one of the criteria to evaluate the satisfaction of the trafficnetwork. At the same time, f_(k,t) ^(road) may also affect the averagearrival rate λ_(i,t) and the charge power P_(i,t) ^(CS) of to-be-chargedvehicles at the node i in each period, and the number of chargingdevices to be configured at the charging station. It is assumed hereinthat λ_(i,t) is directly proportional to the traffic flow intercepted bythe charging station and the EV travel ratio.

Calculate an equivalent charging load according to the traffic flowintercepted by the single charging station in the following calculationmanners:

$\begin{matrix}{{f_{i,t}^{CS} = {\sum\limits_{k \in \Omega_{od}}{f_{k,t}^{road}x_{k,i}^{road}x_{i}^{CS}}}},{i \in \Omega},{t \in T}} & (5) \\{{\lambda_{i}^{RH} = {\max \left\{ {\left. \lambda_{i,t} \middle| \lambda_{i,t} \right. = {{\overset{\sim}{F}}^{CS}{\frac{\sigma_{t}}{\sum\limits_{t \in T}\sigma_{t}} \cdot \frac{f_{i,t}^{CS}}{\sum\limits_{i \in \Omega}f_{i,t}^{CS}}}}} \right\}}},{i \in \Omega}} & (6) \\{{P_{i,t}^{CS} = {p^{CS}\frac{\lambda_{i,t}}{\mu}}},{i \in \Omega},{t \in T}} & (7)\end{matrix}$

in the formula (5), f_(i,t) ^(CS) is a traffic flow intercepted by anode i in a period t; x_(k,i) ^(road) is a binary variable of whetherthe path k passes through the node i; x_(i) ^(CS) is a binary variableof whether a charging station is constructed at the node i; Ω is a setof network nodes; λ_(i,t) is the number of electric vehicles arriving atthe charging station located at the node i at time t to receive acharging service; in the formula (6), P_(i,j) ^(CS) is a charge power ofthe node i at the time t; λ_(i) ^(RH) is an average arrival rate ofto-be-charged vehicles at the node i during rush hours, i.e. the numberof EVs arriving at the charging station to receive the charging serviceper unit of time; {tilde over (F)}^(CS) is a total daily chargingfrequency demand of an EV charging station and needs to be calculatedaccording to W_(B) in the formula (2); {circumflex over(F)}^(CS)=W_(B)/preset maximum battery pack capacity, and in aparticular example, the preset maximum battery pack capacity=90 Ah;W_(B) is a charging capacity; in the formula (7), p^(CS) is a chargepower of a single charging device; and μ is an average service rate of asingle device, in units of vehicles per hour.

Step S13: For a charging station, the level of service is largelydetermined by the average charging waiting time of drivers during rushhours. When the number of charging devices increases, the queuingproblem at charging stations can be alleviated and the waiting time maybe shortened, but the investment cost of the whole system may beincreased. Therefore, the number of devices in each charging station canbe configured by setting a threshold of the average charging waitingtime and establishing relevant constraints, so as to achieve optimalinvestment in charging devices. It is assumed that an arrival processand charging service time of the to-be-charged vehicles at the chargingstation are simulated by using Poisson distribution and negativeexponential distribution respectively. Transform, based on the M/M/squeuing model, a capacity determination problem of a charging stationinto the following nonlinear integer planning problems:

$\begin{matrix}{\min \; z_{i}^{CS}} & (8) \\{s.t.\left\{ {\begin{matrix}{W_{i}^{RH} < W^{allowed}} \\{z_{i}^{CS} \geq \frac{\lambda_{i}^{RH}}{\mu}}\end{matrix},{\forall{i \in \Omega}}} \right.} & (9) \\{{W_{i}^{RH} = {P_{i}^{non}\frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{z_{i}^{CS}}\rho_{i}^{RH}}{{{\lambda_{i}^{RH}\left( z_{i}^{CS} \right)}!}\left( {1 - \rho_{i}^{RH}} \right)^{2}}}},{\lambda_{i}^{RH} \neq 0}} & (10) \\{P_{i}^{non} = \left\lbrack {{\sum\limits_{n = 0}^{z_{i}^{CS} - 1}\frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{n}}{n!}} + \frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{z_{i}^{CS}}}{{\left( z_{i}^{CS} \right)!}\left( {1 - \rho_{i}^{RH}} \right)}} \right\rbrack^{- 1}} & (11) \\{\rho_{i}^{RH} = \frac{\lambda_{i}^{RH}}{z_{i}^{CS}\mu}} & (12)\end{matrix}$

in the formulas: z_(i) ^(CS) is the number of charging devicesconfigured for the node i, which is multiplied by p^(CS) s to obtain thecapacity of the charging station at node i; W_(i) ^(RH) and W^(aloWed)are an average waiting time for receiving a charging service during rushhours and a threshold thereof respectively; P_(i) ^(noon) theprobability that charging station devices at the node i are all idle;and ρ_(i) ^(RH) is an average device usage rate of the node i duringrush hours.

Behavioral scientists have found upon study that a person who stays inline for an average of more than 40 min or waits for an average of morethan 10 min may get annoyed and leave. Considering the particularity ofEV charging time, the threshold may be set to 0.1 h in the firstconstraint of the formula (9). On the other hand, the value of z_(i)^(cs) has to meet the most basic charging frequency demand in order toensure that an infinite long queue may not be formed, so the secondconstraint of the formula (9) needs to be set.

According to the above analysis, a core decision variable of thecharging station location and capacity determination model considering atraffic flow is x_(i) ^(cs). The optimization process not only directlyaffects a satisfaction index of the traffic network, but also affectsthe level of the charge power and investment cost of the chargingdevice. Therefore, the model may well associate a traffic demand with apower load, and further reflect a closely linked and mutuallyinfluencing relationship between a power distribution network and atraffic network.

In this embodiment, the distributed generation (including wind power andphotovoltaic) has obvious intermittency and randomness, and is greatlyrestricted by meteorological conditions, but its output also has certainregularity with the change of seasons and time series. In terms ofseasonal characteristics, WG output reaches its maximum in winter andits minimum in summer, while PV is just the opposite. In terms oftime-series characteristics, WG reaches its maximum in the evening,while PV has a greater output at noon. Residential load, commercialload, and industrial load in daily life also have similar time-seriesrules, but the three main loads are different in nature and their changerules are not the same. Therefore, a typical day may be selected in fourseasons respectively, and 24 moments may be used to simulate DG outputand load power scenarios in each season, which are combined into 96scenarios in the whole year. Curves of time-series characteristics ofwind-solar output and three main loads are shown in FIG. 1 to FIG. 5.Step S2 particularly includes:

establishing the active distribution network model, and sampling, basedon a time series method, typical output and different types of typicalload curves of distributed generation including wind power andphotovoltaic, to obtain a DG output value DG(t) and a load value P_(L,i)^((t)) of the node i at the time t; and establishing an energy storagemodel based on an equivalent load principle, an energy storage elementadjusting strategy being as follows:

In this embodiment, energy is stored through an accumulator, and acoordinated optimization strategy for energy storage based on anequivalent load is proposed. It is assumed that the output power of windand photovoltaic power generation is constant in each scenario, and atypical day in the time-series characteristics is used as a cycle forstudy. Firstly, calculate an equivalent load P_(iqu) and an averageequivalent load Pa of the node i at the time t,

$\begin{matrix}{{P_{eqi}(t)} = {{P_{Li}(t)} - {P_{DGi}(t)}}} & (13) \\{P_{avi} = {\sum\limits_{t = 1}^{24}{{P_{eqi}(t)}/24}}} & (14)\end{matrix}$

in the formulas: P_(Li)(t) and P_(DGi)(t) represent a load value and aDG output value of the node i at the time t.

The coordinated optimization strategy based on energy storageparticularly includes the following contents:

(1) If P_(eqi) is far less than P_(avi), it indicates that the electricload is at the trough, and the accumulator can store the excess DG powerby charging. Therefore, when P_(eqi)(t)+ΔP<<P_(avi), an accumulator ischarged, and ΔP₁ is a charge power.

(2) After charge for a period of time, if P_(eqi) is slightly less thanP_(avi), it indicates that output and demand are close to equilibrium.In this case, in order to suppress the fluctuation of the equivalentload, charging conditions need to be adjusted. If|P_(eqi)(t)+ΔP₁P_(avi)|≤δP_(avi) is met, the accumulator is charged; δrepresents a fluctuation coefficient of P_(eqi) around a mean valuethereof, which is set to 0.8 in this embodiment.

(3) If P_(eqi) is far greater than P_(avi), it indicates that theelectric load is at the peak and the accumulator needs to release power.Therefore, when P_(eqi)(t)−ΔP₂≥≥P_(avi), the accumulator is discharged,and ΔP₂ is a discharge power.

(4) After discharge for a period of time, if P_(eqi) is slightly greaterthan P_(avi), it indicates that output and demand are close toequilibrium. In this case, in order to suppress the fluctuation of theequivalent load, discharging conditions need to be adjusted. If|P_(eqi)(t)−ΔA−P_(avi)|≤δP_(avi) is met, the accumulator is discharged.

In this embodiment, step S3 particularly includes:

an objective function of the nested planning model being:

$\begin{matrix}{\mspace{79mu} {\min \left\{ \begin{matrix}{f_{1} = {{\frac{{r\left( {1 + r} \right)}^{\eta}}{\left( {1 + r} \right)^{\eta} - 1}C^{inv}} + C^{ope}}} \\{{f_{2} = {\sum\limits_{s = 1}^{96}{\sum\limits_{i = 1}^{n}{U_{s,i}^{level}/\left( {96 \cdot n} \right)}}}},{i \in \Omega},{s \in \Omega_{s}}} \\{{f_{3} = {1/\left( {365 \cdot {\sum\limits_{t = 1}^{24}{\sum\limits_{k \in \Omega_{od}}{f_{k,t}^{road}x_{k}^{load}}}}} \right)}},{t \in T}}\end{matrix} \right.}} & (15) \\{C^{inv} = {{p^{DG}\left( {{c_{1}^{PV}{\sum\limits_{j \in \Omega^{PV}}N_{j}}} + {c_{1}^{WG}{\sum\limits_{k \in \Omega^{WG}}N_{j}}}} \right)} + {c^{CS}{\sum\limits_{i \in \Omega}{z_{i}^{CS}x_{i}^{CS}}}} + {\sum\limits_{k \in \Omega^{BS}}{x_{k}^{BS}\left( {{c_{1}^{BS}S_{\max}^{BS}} + {c_{2}^{BS}P_{\max}^{BS}}} \right)}}}} & (16) \\{C^{ope} = {{c_{2}^{PV}{\sum\limits_{s \in \Omega_{s}}{\sum\limits_{j \in \Omega^{PV}}{\Delta \; t_{s}P_{s,j}^{PV}}}}} + {c_{2}^{WG}{\sum\limits_{s \in \Omega_{s}}{\sum\limits_{j \in \Omega^{WG}}{\Delta \; t_{s}P_{s,j}^{WG}}}}} + {\sum\limits_{s \in \Omega_{s}}{{f_{e}(s)}{P_{em}(s)}\Delta \; t_{s}}}}} & (17) \\{\mspace{79mu} {{P_{em}(s)} = {{\sum\limits_{i = 1}^{n}\left( {P_{s,i}^{L} + P_{s,i}^{CS}} \right)} - \left( {{\sum\limits_{j \in \Omega^{PV}}P_{s,j}^{PV}} + {\sum\limits_{j \in \Omega^{WG}}P_{s,j}^{WG}}} \right) + P_{s}^{loss}}}} & (18) \\{\mspace{79mu} {U_{s,i}^{level} = \left\{ \begin{matrix}{\frac{V_{s,i} - 1}{V^{\min} - 1},{V^{\min} < V_{s,i} \leq 1}} \\{\frac{V_{s,i} - 1}{V^{\max} - 1},{1 < V_{s,i} < V^{\max}}} \\{1.0,{{V_{s,i} \geq V^{\max}};{V_{s,i} \leq V^{\min}}}}\end{matrix} \right.}} & (19)\end{matrix}$

in the formulas: f₁ denotes an economic cost, including a constructioncost C^(inv) and an operation cost C^(rope); r is a discount rate; η isan investment life; f₂ denotes a voltage quality index; U_(s,i) ^(level)is a voltage quality evaluation function value of the node i in ascenario s; n is the total number of network nodes; Ω denotes a set ofnodes; Ω_(S) is a set of scenarios; f₃ denotes a traffic networksatisfaction index; Ω_(bd) is a set of shortest paths from any startingpoint o to any ending point d in the traffic network; f_(k,t) ^(road)denotes a per-unit value of a one-way traffic flow demand of theshortest path k in a period t; x_(k) ^(load) denotes a binary variableof whether a flow on the path k is intercepted by a charging state; T isa set of periods; p^(DG) is a DG unit capacity; x_(i) ^(CS) is a binaryvariable of whether a charging station is constructed at the node i; c₁^(PV) and c₁ ^(WG) are investment costs per unit capacity ofphotovoltaic and wind power generation respectively; Ω^(PV) and Ω^(WG)are sets of nodes for mounting photovoltaic and fans; N_(j) is thenumber of DGs of the j^(th) mounting node; c^(CS) is investment cost ofeach charging device; x_(k) ^(BS) is a binary variable of whether a nodek is put into an energy storage device; Ω^(BS) is a set of nodes formounting energy storage; c₁ ^(BS) and c₂ ^(BS) are a unit capacity costand a charge-discharge power cost of the energy storage devicerespectively; S_(max) ^(BS) and P_(max) ^(BS) are maximum energy storagecapacity and maximum charge-discharge power respectively; c₂ ^(PV) andc₂ ^(WG) are unit operation costs of photovoltaic and wind powergeneration respectively; Δt_(s) is an annual cumulative operation timeof a distribution network in a scenario s; P_(s,j) ^(PV) and P_(s,j)^(WG) are outputs of the j^(th) PV or WG in the scenario s; f_(e)(s) andP_(em)(s) are electricity price and electric power demands in thescenario s respectively; P_(s,i) ^(L) and are a load power and an EVcharge power of the node i in the scenario s; P_(s) ^(loss) is electricenergy loss in the scenario s; V_(s,i) is a voltage amplitude of thenode i in the scenario s; and V^(min) and V_(max) are an allowable lowerlimit and an allowable upper limit of a node voltage respectively.

Constraints of the nested planning model include traffic networkconstraints and power grid constraints, and the traffic networkconstraints are as follows:

$\begin{matrix}\left\{ {\begin{matrix}{W_{i}^{RH} < W^{allowed}} \\{z_{i}^{CS} \geq \frac{\lambda_{i}^{RH}}{\mu}}\end{matrix},{\forall{i \in \Omega}}} \right. & (20) \\{{\sum\limits_{i \in \Omega}x_{i}^{CS}} \leq N^{CS}} & (21) \\{{{\sum\limits_{i \in \Omega}{\sum\limits_{k \in \Omega_{od}}{f_{k,t}^{road}x_{k,i}^{road}x_{i}^{CS}}}} \geq {\sum\limits_{k \in \Omega_{od}}f_{k,t}^{road}}},{\forall{t \in T}}} & (22) \\{{W_{i}^{RH} = {P_{i}^{non}\frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{z_{i}^{CS}}\rho_{i}^{RH}}{{{\lambda_{i}^{RH}\left( z_{i}^{CS} \right)}!}\left( {1 - \rho_{i}^{RH}} \right)^{2}}}},{\lambda_{i}^{RH} \neq 0}} & (23) \\{P_{i}^{non} = \left\lbrack {{\sum\limits_{n = 0}^{z_{i}^{CS} - 1}\frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{n}}{n!}} + \frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{z_{i}^{CS}}}{{\left( z_{i}^{CS} \right)!}\left( {1 - \rho_{i}^{RH}} \right)}} \right\rbrack^{- 1}} & (24) \\{\rho_{i}^{RH} = \frac{\lambda_{i}^{RH}}{z_{i}^{CS}\mu}} & (25)\end{matrix}$

in the formulas: z_(i) ^(CS) is the number of charging devicesconfigured for the node i, which is multiplied by p^(CS) to obtain acharge power of a single charging device at the node i; λ_(i) ^(RH) isan average arrival rate of to-be-charged vehicles at the node i duringrush hours, i.e. the number of EVs arriving at the charging station toreceive the charging service per unit of time; x_(k,i) ^(road) denotes abinary variable of whether a flow on the path k can be intercepted by acharging station; Ω_(bd) is a set of shortest paths from any startingpoint o to any ending point d in the traffic network; W_(i) ^(RH) andW^(allowed) are an average waiting time for receiving a charging serviceduring rush hours and a threshold thereof respectively; P_(i) ^(noon) isthe probability that charging station devices at the node i are allidle; ρ_(i) ^(RH) is an average device usage rate of the node i duringrush hours; N^(CS) is the maximum number of charging stations to beconstructed; and μ is an average service rate of a single device;

the power grid constraints are as follows:

power flow constraints of the power distribution network:

$\begin{matrix}\left\{ {{\begin{matrix}{{P_{s,i}^{L} + P_{s,i}^{CS} - P_{s,i}^{DG}} = {V_{s,i}{\sum\limits_{j = 1}^{n}{V_{s,j}\left( {{G_{ij}\cos \; \delta_{s,{ij}}} + {B_{ij}\sin \; \delta_{s,{ij}}}} \right)}}}} \\{{Q_{s,i}^{L} + Q_{s,i}^{DG}} = {V_{s,i}{\sum\limits_{j = 1}^{n}{V_{s,j}\left( {{G_{ij}\sin \; \delta_{s,{ij}}} + {B_{ij}\cos \; \delta_{s,{ij}}}} \right)}}}}\end{matrix}{\forall{s \in \Omega_{s}}}},{i \in \Omega}} \right. & (26)\end{matrix}$

scenario chance constraints:

$\begin{matrix}{{{\Pr \left\{ {{V^{\min} \leq V_{s,i} \leq V^{\max}},{{P_{s,{ij}}} \leq P_{ij}^{\max}}} \right\}} = {\frac{K_{s}}{96} \geq {\gamma {\forall{i \in \Omega}}}}},{\forall{{ij} \in \Omega^{Line}}}} & (27)\end{matrix}$

DG mounting capacity constraints:

$\begin{matrix}\left\{ \begin{matrix}{{0 \leq P_{s,j}^{PV} \leq {\overset{\_}{P}}_{s,j}^{PV}},{\forall{s \in \Omega_{s}}},{j \in \Omega^{PV}}} \\{{0 \leq P_{s,j}^{WG} \leq {\overset{\_}{P}}_{s,j}^{WG}},{\forall{s \in \Omega_{s}}},{j \in \Omega^{WG}}} \\{{\sum\limits_{s \in \Omega_{s}}\left( {P_{s,j}^{PV} + P_{s,j}^{WG}} \right)} \leq {ɛ{\sum\limits_{s \in \Omega_{s}}{\sum\limits_{i = 1}^{n}P_{s,i}^{L}}}}}\end{matrix} \right. & (28)\end{matrix}$

energy storage capacity and charge-discharge power constraints:

$\begin{matrix}\left\{ {\begin{matrix}{{0 \leq S_{k}^{BS} \leq S_{\max}^{BS}},} \\{{0 \leq P_{k}^{BS} \leq P_{\max}^{BS}},}\end{matrix}{\forall{k \in \Omega^{BS}}}} \right. & (29)\end{matrix}$

in the formulas: Q_(s,i) ^(L) is a reactive load of the node i in thescenario s; P_(s,i) ^(DG) and Ω_(s,i) ^(DG) are DG active and reactiveoutputs of the node i in the scenario s; V_(s,j) is a voltage amplitudeof a node j in the scenario s; G_(ij) and B_(ij) are real part andimaginary part of network admittances respectively; S_(s,ij) is avoltage phase angle difference of the nodes i and j in the scenario s;P_(s,ij) and P_(ij) ^(max) are a power flowing through a line ij and apower limit; K_(s) is the number of scenarios meeting chanceconstraints; γ is a confidence coefficient; Ω^(Line) is a set of powerdistribution network lines; P _(s,j) ^(PV) and P _(s,j) ^(WG) are outputupper limits of PV and WG respectively; ε is a maximum penetration rateof DG access; and S_(k) ^(BS) and area current device capacity and acharge-discharge power of an energy storage node k respectively.

In order to demonstrate the superiority of the planning model of thepresent disclosure, in this embodiment, a coupling topology structure oftraffic network-power distribution network as shown in FIG. 6 is used tosimulate and verify the model of the present disclosure.

In a simulation example of this embodiment, in combination withengineering practice, a unit capacity of a DG node is set to 0.1 MW, thenumber of installations is limited to 20, the maximum energy storagecapacity is 3 MWh, and a single maximum charge and discharge power ofthe accumulator is 0.3 MW. A constraint range of a node voltageamplitude is 0.95 to 1.05 pu. The number of locations for chargingstations is limited to 8.

An NSGA-II algorithm is used to solve the simulation example of thisembodiment. Since the NSGA II algorithm is an existing very maturesolution algorithm, a detailed calculation method of the algorithm isnot repeated in this application. A maximum iteration number of the NSGAII algorithm is set to 50, a population size to 150, a crossover rate to0.9, a variation rate to 0.1, and a polynomial variation index to 20.Parameters related to economic costs, vehicle flow weights at trafficnodes and the travel ratio of EVs in each period are shown in Table 1 toTable 3.

TABLE 1 Parameters related to economic costs Parameter Value ParameterValue Planned investment life 10 years Discount rate 10% WG constructioncost 873.6 $/kW WG operation cost 0.022 $/kWh PV construction cost 1164.8 $/kW PV operation cost 0.03 $/kWh Energy storage power cost 730.9$/kW Energy storage capacity cost 208.2 $/kWh Charging device cost 5.96× 10⁴ $ Calculation of 0.1627 per vehicle depreciation factorElectricity price 30 $/MW² Electricity price 15 $/MW parameter θ₂parameter θ₁

TABLE 2 Vehicle flow weights at traffic nodes Node number Weight 1 0.542 0.8 3 1.2 4 0.87 5 1.26 6 1.7 7 1.5 8 0.94 9 0.97 10 0.54 11 0.35 120.34 13 0.15 14 0.35 15 0.28 16 0.6 17 0.28 18 0.37 19 1.08 20 0.95 210.62 22 0.55 23 0.65 24 0.34 25 0.45 26 0.63 27 1.1 28 0.54 29 0.6 300.32 31 0.21 32 0.34 33 0.28

TABLE 3 Travel ratio of electric vehicles in each period PeriodPercentage 1 0.44 2 0.21 3 0.11 4 0.07 5 0.19 6 0.81 7 2.54 8 6.13 97.69 10 5.61 11 6.45 12 6.57 13 6.51 14 6.91 15 6.98 16 7.21 17 8.78 189.05 19 5.28 20 4.41 21 2.78 22 2.06 23 1.95 24 1.26

Electric vehicle related information simulating the system is shown inTable 4. The transformer efficiency and the charger efficiency used inthe charging station herein are 95% and 90% respectively. According tothe calculation of formulas (A1) and (A2), the total daily demand ofbattery packs in the region is 2284, and the average daily chargingcapacity demand is 11,086.1 kWh. It is assumed that the single chargingcapacity of each EV is 30 kWh and the charge power of a single chargingdevice is 60 kW, the total daily charging frequency of all chargingstations is 370 times, and an average service rate of a single device is0.5.

TABLE 4 Regional electric vehicle related information Number of Stock ofDaily vehicle- electric mileage mounted Battery vehicles/ Daily upon onebattery Attendance replacement per EV type mileage/km charging/km packs/rate/% ratio/% vehicle Bus 280 140 4 100 100 36 Service car 200 100 371.4 100 28 Taxi 300 150 4 75 100 54 Private car 50 100 3 75 50 2032Other vehicles 90 60 2 50 20 453 (sanitation vehicles, postal vehicles,etc.)

The simulation example of this embodiment relates to two parts: a powerdistribution system and a traffic network, and the solution process isshown in FIG. 7.

(1) Data required by planning is inputted, a daily charging demand ofcharging stations is calculated based on various kinds of EVinformation, and time-series data of DG and load is simulated.

(2) An initial population is randomly generated, and an objectivefunction value of individuals satisfying chance constraints iscalculated based on the coupled power distribution network and trafficnetwork.

(3) Fast non-dominated sorting is performed on the initial population,and a progeny population is obtained by selecting a high-quality maleparent for genetic manipulation based on sequence and crowdinginformation of individuals.

(4) Based on the coupled network, an objective function value of theprogeny population is calculated, then all progeny individuals are mixedwith parental individuals, and an elitist strategy is adopted to prunethe population size to obtain a new male parent.

(5) It is judged whether the maximum number of iterations is reached. Ifyes, exit the calculation; otherwise, go back to step (3) and continuethe iteration.

(6) After the iteration, repeated solutions in the final population aredeleted, then target values of the remaining schemes are dimensionless,and standard deviations of targets of all schemes are calculated.Finally, based on a mean square deviation method, weights of respectiveobjective functions are set according to the principle of proportionalallocation, and an optimal compromise scheme is determined by atechnique for order preference by similarity to an ideal solution(TOPSIS). Its particular operation process may be obtained withreference to references. As the TOPSIS algorithm is a relatively maturetechnology, it is not repeated in this application.

Calculation results of this embodiment areas shown in Table 5 and Table6.

TABLE 5 DG node configuration results Configu- Configu- ration Whetherto ration Whether to capacity/ install energy capacity/ install energyWG MW storage WG MW storage 4 1.7 ✓ 11 1.7 ✓ 21 0 x 15 1.8 ✓ 25 1.4 ✓ 200.2 ✓ 27 2.0 ✓ 31 2.0 ✓

TABLE 6 Planning results of electric vehicle charging stationsConfiguration Configuration Location node capacity/MW Location nodecapacity/MW 3 0.24 19 0.18 6 0.30 20 0.30 7 0.18 26 0.30 9 0.24 28 0.24

The economic cost corresponding to the optimal scheme is 14.114 milliondollars, the voltage quality index is 0.061 pu, and the trafficsatisfaction index is 1.3×10⁻⁶ pu, that is, the annual interceptedtraffic flow value is 7.68×10⁵ pu.

Planning analysis results of electric vehicle charging stations areshown in FIG. 8 to FIG. 10.

From the perspective of planning results, in order to capture as muchtraffic flow in the traffic network as possible and meet EV chargingdemands of users to the maximum extent, station nodes are generallyselected in positions with a large vehicle flow weight (such as nodes 3,6, and 7) or hub positions of the traffic network (such as nodes 19, 20,and 26). In Table 6, the sum of vehicle flow weights at the locationnode is 8.57, accounting for 39.6% of the weights of the entire trafficnetwork. At the same time, the charging stations can capture 190.54 puof the daily traffic flow during rush hours, accounting for 90.9% of thetotal traffic flow during rush hours. As can be seen, the satisfactionindex constructed in the model can effectively help station constructionnodes to capture as much traffic flow as possible and provide chargingservices for more EV users without changing the original driving path.

On the other hand, EV charging may increase the charging load of thestation construction node and change the load time-seriescharacteristics of the node. Taking a node 19 as an example, the loadtime-series curve before and after EV charging is considered as shown inFIG. 8.

As shown in FIG. 8, considering EV charging is equivalent to raising theload curve of the station construction node, making the load levelheavier. At the same time, the travel ratio of EVs in each period mayalso affect the characteristics of the time-series curve. With referenceto Table 3, electric vehicles mainly travel between 8:00 and 20:00.Therefore, in FIG. 8, there are more load increments in thecorresponding periods of typical days in the seasons, especially at18:00 in the peak hour, when the load power reaches its peak.

Location and capacity determination planning of EV charging stations maynot only change the load time-series characteristics of stationconstruction nodes, but also change the load level of the entiredistribution network nodes, thus affecting the voltage quality of thenodes. Taking the peak period in spring as an example, the system loadlevel before and after EV charging is considered as shown in FIG. 9, andthe node voltage amplitude distribution of the corresponding scenario isshown in FIG. 10.

As can be seen from FIG. 9, during the peak travel period of electricvehicles, the load powers of eight station construction nodes allincrease significantly, especially the load of the node 6 increases bymore than three times, and the load of nodes 9, 26, and 28 increased bynearly two times. The eight nodes are basically distributed in front andmiddle ends of the circuit in the power network, which is bound toincrease the voltage drop in the front and middle ends of each branch.

In FIG. 10, the large increase of the load on nodes 6 and 9 causes thevoltage to significantly drop in the branch between nodes 3 to 18, andthe large increase of the load on nodes 26 and 28 causes the voltage tosignificantly drop in the branch between nodes 26 to 33. The voltagequality index proposed herein is used to evaluate the voltage level ofthe system in the two cases. The estimated value before EV charging is0.0824, and the estimated value after consideration of the charging loadis 0.1459, which decreases by 77.1%. As can be seen, this part ofcharging load may lead to a greater impact on the network during rushhours, reducing the node voltage level of the system.

The above are only preferred embodiments of the present disclosure, andany equal changes and modifications made in accordance with the scope ofthe invention application patent all come within the scope of thepresent disclosure.

1. A method for establishing an active distribution network planningmodel considering location and capacity determination of an electricvehicle charging station, comprising the following steps: step S1:establishing a traffic network, and establishing, based on an N/M/squeuing model and a flow capturing location model, a traffic networkcomprising an electric vehicle charging station; step S2: establishingan active distribution network model, and establishing a distributedgeneration and load time-series model based on a time series method; andestablishing an energy storage model based on an equivalent loadprinciple; and step S3: converting a traffic flow of electric vehiclesinto an equivalent load of an equivalent charging station, coupling thetraffic network with a power grid, and establishing an activedistribution network nested planning model considering the trafficnetwork.
 2. The method for establishing an active distribution networkplanning model considering location and capacity determination of anelectric vehicle charging station according to claim 1, wherein step S1particularly comprises: step S11: calculating an EV charging capacitydemand; calculating a battery pack quantity demand; $\begin{matrix}{N_{B} = {\sum\limits_{i = 1}^{5}\left( {N_{EVi}\frac{L_{di}}{L_{0i}}a_{i}b_{i}K_{EVdi}} \right)}} & (1)\end{matrix}$ in the formula: N_(B) is a daily demand for battery packs;N_(EVi) is a stock of an i^(th)-type EV; L_(di) and L_(0i) arerespectively an average daily mileage of the i^(th)-type EV and adistance at which the i^(th)-type EV travels on a full charge; anda_(i), b_(i), and K_(EVdi) are respectively attendance rates, a batteryreplacement ratio, and the number of battery packs per vehicle for thei^(th)-type EV; the charging capacity demand is:W _(B) =N _(B) P _(C) ^(t) _(charge)/(η_(tran)η_(charge))  (2) in theformula: η_(tran) is transformer efficiency; η_(charge) is chargerefficiency; P_(c) denotes an average charge power; and t_(change)denotes a charging time; step S12: establishing a charging stationlocation and capacity determination model; calculating a traffic flowF_(CS) annually intercepted by a system-wide charging station by using agravity space interaction model in combination with a Floyd algorithm;of which a calculation formula is as follows: and calculating a trafficflow intercepted by a single charging station according to the followingformulas: $\begin{matrix}{{f_{k,t}^{road} = {\frac{\omega_{ko}\omega_{kd}}{D_{k}^{1.5}} \cdot \frac{\sigma_{t}}{\sigma_{RH}}}},{k \in \Omega_{od}},{t \in T}} & (3) \\{F_{CS} = {365 \cdot {\sum\limits_{t = 1}^{24}{\sum\limits_{k \in \Omega_{od}}{f_{k,t}^{road}x_{k}^{load}}}}}} & (4)\end{matrix}$ in the formula (3): f_(k,l) ^(road) denotes a per-unitvalue of a one-way traffic flow demand of the shortest path k in aperiod t; ω_(ko) and ω_(kd) are traffic demand weights of a startingpoint and an ending point of the path k respectively, used to indicatebusyness degrees of traffic nodes; D_(k) is a per-unit value of thelength of the path k; σ_(t) and σ_(RH) are travel ratios of EV users ina period t and a peak hour h respectively; Ω_(bd) is a set of shortestpaths from any starting point o to any ending point d in the trafficnetwork and is obtained according to the Floyd algorithm; T is a set ofperiods; and x_(k) ^(load) indicates a binary variable of whether a flowon the path k can be intercepted by a charging station, if the path kpasses through the charging station, the variable is 1, and otherwise,the variable is 0; calculating an equivalent charging load according tothe traffic flow intercepted by the single charging station in thefollowing calculation manners: $\begin{matrix}{{f_{i,t}^{CS} = {\sum\limits_{k \in \Omega_{od}}{f_{k,t}^{road}x_{k,i}^{road}x_{i}^{CS}}}},{i \in \Omega},{t \in T}} & (5) \\{{\lambda_{i}^{RH} = {\max \left\{ {\left. \lambda_{i,t} \middle| \lambda_{i,t} \right. = {{\overset{\sim}{F}}^{CS}{\frac{\sigma_{t}}{\sum\limits_{t \in T}\sigma_{t}} \cdot \frac{f_{i,t}^{CS}}{\sum\limits_{i \in \Omega}f_{i,t}^{CS}}}}} \right\}}},{i \in \Omega}} & (6) \\{{P_{i,t}^{CS} = {p^{CS}\frac{\lambda_{i,t}}{\mu}}},{i \in \Omega},{t \in T}} & (7)\end{matrix}$ in the formula (5), f_(i,t) ^(CS) is a traffic flowintercepted by a node i in a period t; x_(k,i) ^(road) is a binaryvariable of whether the path k passes through the node i; x_(i) ^(CS) isa binary variable of whether a charging station is constructed at thenode i; Ω is a set of network nodes; λ_(i,t) is the number of electricvehicles arriving at the charging station located at the node i at timet to receive a charging service; in the formula (6), P_(i,t) ^(CS) is acharge power of the node i at the time t; λ_(i) ^(RH) is an averagearrival rate of to-be-charged vehicles at the node i during rush hours,i.e. the number of EVs arriving at the charging station to receive thecharging service per unit of time; {tilde over (F)}^(CS) is a totaldaily charging frequency demand of an EV charging station and needs tobe calculated according to W_(B) in the formula (2); {tilde over(F)}^(CS)=W_(B)/preset maximum battery pack capacity; W_(B) is acharging capacity; in the formula (7), p^(CS) is a charge power of asingle charging device; and μ is an average service rate of a singledevice, in units of vehicles per hour; and step S13: transforming, basedon the M/M/s queuing model, a capacity determination problem of acharging station into the following nonlinear integer planning problems:$\begin{matrix}{\min \; z_{i}^{CS}} & (8) \\{s.t.\left\{ {\begin{matrix}{W_{i}^{RH} < W^{allowed}} \\{z_{i}^{CS} \geq \frac{\lambda_{i}^{RH}}{\mu}}\end{matrix},{\forall{i \in \Omega}}} \right.} & (9) \\{{W_{i}^{RH} = {P_{i}^{non}\frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{z_{i}^{CS}}\rho_{i}^{RH}}{{{\lambda_{i}^{RH}\left( z_{i}^{CS} \right)}!}\left( {1 - \rho_{i}^{RH}} \right)^{2}}}},{\lambda_{i}^{RH} \neq 0}} & (10) \\{P_{i}^{non} = \left\lbrack {{\sum\limits_{n = 0}^{z_{i}^{CS} - 1}\frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{n}}{n!}} + \frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{z_{i}^{CS}}}{{\left( z_{i}^{CS} \right)!}\left( {1 - \rho_{i}^{RH}} \right)}} \right\rbrack^{- 1}} & (11) \\{\rho_{i}^{RH} = \frac{\lambda_{i}^{RH}}{z_{i}^{CS}\mu}} & (12)\end{matrix}$ in the formulas: z_(i) ^(CS) is the number of chargingdevices configured for the node i, which is multiplied by p^(CS) toobtain the capacity of the charging station at node i; and W_(i) ^(RH)and W^(allowed) are an average waiting time for receiving a chargingservice during rush hours and a threshold thereof respectively; P_(i)^(non) is the probability that charging station devices at the node iare all idle; and ρ_(i) ^(Rh) is an average device usage rate of thenode i during rush hours.
 3. The method for establishing an activedistribution network planning model considering location and capacitydetermination of an electric vehicle charging station according to claim1, wherein step S2 particularly comprises: establishing the activedistribution network model, and sampling, based on a time series method,typical output and different types of typical load curves of distributedgeneration comprising wind power and photovoltaic, to obtain a DG outputvalue P_(DGi)(t) and a load value P_(L,i) (t) of the node i at the timet; and establishing an energy storage model based on an equivalent loadprinciple, an energy storage element adjusting strategy being asfollows: calculating an equivalent load P_(eqi) and an averageequivalent load P_(avi) of the node i at the time t, $\begin{matrix}{{P_{eqi}(t)} = {{P_{Li}(t)} - {P_{DGi}(t)}}} & (13) \\{P_{avi} = {\sum\limits_{t = 1}^{24}{{P_{eqi}(t)}/24}}} & (14)\end{matrix}$ in the formulas: P_(Li)(t) and P_(DGi)(t) represent a loadvalue and a DG output value of the node i at the time t; and the energystorage element adjusting strategy is particularly as follows: whenP_(eqi)(t)+ΔPx₁>>P_(avi), an accumulator is charged, and ΔP₁ is a chargepower; if |P_(eqi)(t)+Δv_(P)ΔS−|δP_(avi) coefficient of P_(eqi) around amean value thereof, when P_(eqi)(t)−ΔP₂>>P_(avi) the accumulator isdischarged, and ΔP₂ is a discharge power; and if|P_(eqi)(t)−ΔP−P_(avi)|≤δP_(avi) is met, the accumulator is discharged.4. The method for establishing an active distribution network planningmodel considering location and capacity determination of an electricvehicle charging station according to claim 1, wherein step S3particularly comprises: an objective function of the nested planningmodel being: $\begin{matrix}{\mspace{79mu} {\min \left\{ \begin{matrix}{f_{1} = {{\frac{{r\left( {1 + r} \right)}^{\eta}}{\left( {1 + r} \right)^{\eta} - 1}C^{inv}} + C^{ope}}} \\{{f_{2} = {\sum\limits_{s = 1}^{96}{\sum\limits_{i = 1}^{n}{U_{s,i}^{level}/\left( {96 \cdot n} \right)}}}},{i \in \Omega},{s \in \Omega_{s}}} \\{{f_{3} = {1/\left( {365 \cdot {\sum\limits_{t = 1}^{24}{\sum\limits_{k \in \Omega_{od}}{f_{k,t}^{road}x_{k}^{load}}}}} \right)}},{t \in T}}\end{matrix} \right.}} & (15) \\{C^{inv} = {{p^{DG}\left( {{c_{1}^{PV}{\sum\limits_{j \in \Omega^{PV}}N_{j}}} + {c_{1}^{WG}{\sum\limits_{k \in \Omega^{WG}}N_{j}}}} \right)} + {c^{CS}{\sum\limits_{i \in \Omega}{z_{i}^{CS}x_{i}^{CS}}}} + {\sum\limits_{k \in \Omega^{BS}}{x_{k}^{BS}\left( {{c_{1}^{BS}S_{\max}^{BS}} + {c_{2}^{BS}P_{\max}^{BS}}} \right)}}}} & (16) \\{C^{ope} = {{c_{2}^{PV}{\sum\limits_{s \in \Omega_{s}}{\sum\limits_{j \in \Omega^{PV}}{\Delta \; t_{s}P_{s,j}^{PV}}}}} + {c_{2}^{WG}{\sum\limits_{s \in \Omega_{s}}{\sum\limits_{j \in \Omega^{WG}}{\Delta \; t_{s}P_{s,j}^{WG}}}}} + {\sum\limits_{s \in \Omega_{s}}{{f_{e}(s)}{P_{em}(s)}\Delta \; t_{s}}}}} & (17) \\{\mspace{79mu} {{P_{em}(s)} = {{\sum\limits_{i = 1}^{n}\left( {P_{s,i}^{L} + P_{s,i}^{CS}} \right)} - \left( {{\sum\limits_{j \in \Omega^{PV}}P_{s,j}^{PV}} + {\sum\limits_{j \in \Omega^{WG}}P_{s,j}^{WG}}} \right) + P_{s}^{loss}}}} & (18) \\{\mspace{79mu} {U_{s,i}^{level} = \left\{ \begin{matrix}{\frac{V_{s,i} - 1}{V^{\min} - 1},{V^{\min} < V_{s,i} \leq 1}} \\{\frac{V_{s,i} - 1}{V^{\max} - 1},{1 < V_{s,i} < V^{\max}}} \\{1.0,{{V_{s,i} \geq V^{\max}};{V_{s,i} \leq V^{\min}}}}\end{matrix} \right.}} & (19)\end{matrix}$ in the formulas: f₁ denotes an economic cost, comprising aconstruction cost C^(iniv) and an operation cost C^(ope); r is adiscount rate; η is an investment life; f₂ denotes a voltage qualityindex; U_(s,i) ^(level) is a voltage quality evaluation function valueof the node i in a scenario s; n is the total number of network nodes; Ωdenotes a set of nodes; Ω_(S) is a set of scenarios; denotes a trafficnetwork satisfaction index; od is a set of shortest paths from anystarting point o to any ending point d in the traffic network; f_(k)^(load) denotes a per-unit value of a one-way traffic flow demand of theshortest path k in a period t; x_(k) ^(load) denotes a binary variableof whether a flow on the path k is intercepted by a charging state; T isa set of periods; p^(DG) is a DG unit capacity; x_(i) ^(CS) is a binaryvariable of whether a charging station is constructed at the node i;c_(i) ^(PV) and c₁ ^(WG) are investment costs per unit capacity ofphotovoltaic and wind power generation respectively; Q and Ω^(WG) aresets of nodes for mounting photovoltaic and fans; N_(j) is the number ofDGs of the j^(th) mounting node; c^(CS) is investment cost of eachcharging device; x_(k) ^(BS) is a binary variable of whether a node k isput into an energy storage device; Ω^(BS) is a set of nodes for mountingenergy storage; c₁ ^(BS) and c₂ ^(BS) re a unit capacity cost and acharge-discharge power cost of the energy storage device respectively;S_(max) ^(BS) and p_(max) ^(BS) are maximum energy storage capacity andmaximum charge-discharge power respectively; c₂ ^(PV) and c₂ ^(WG) areunit operation costs of photovoltaic and wind power generationrespectively; Δt_(s) is an annual cumulative operation time of adistribution network in a scenario s; P_(s,j) ^(PV) and P_(s,j) ^(WG)are outputs of the j^(th) PV or WG in the scenario s; P_(s,i) ^(L)(s)and P_(em)(s) are electricity price and electric power demands in thescenario s respectively; s_(s,i) ^(L) and P_(s,i) ^(CS) are a load powerand an EV charge power of the node i in the scenario s; P_(s) ^(loss) iselectric energy loss in the scenario s; V_(s,i) is a voltage amplitudeof the node i in the scenario s; and V^(min) and V^(max) are anallowable lower limit and an allowable upper limit of a node voltagerespectively; constraints of the nested planning model comprisingtraffic network constraints and power grid constraints, and the trafficnetwork constraints being as follows: $\begin{matrix}\left\{ {\begin{matrix}{W_{i}^{RH} < W^{allowed}} \\{z_{i}^{CS} \geq \frac{\lambda_{i}^{RH}}{\mu}}\end{matrix},{\forall{i \in \Omega}}} \right. & (20) \\{{\sum\limits_{i \in \Omega}x_{i}^{CS}} \leq N^{CS}} & (21) \\{{{\sum\limits_{i \in \Omega}{\sum\limits_{k \in \Omega_{od}}{f_{k,t}^{road}x_{k,i}^{road}x_{i}^{CS}}}} \geq {\sum\limits_{k \in \Omega_{od}}f_{k,t}^{road}}},{\forall{t \in T}}} & (22) \\{{W_{i}^{RH} = {P_{i}^{non}\frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{z_{i}^{CS}}\rho_{i}^{RH}}{{{\lambda_{i}^{RH}\left( z_{i}^{CS} \right)}!}\left( {1 - \rho_{i}^{RH}} \right)^{2}}}},{\lambda_{i}^{RH} \neq 0}} & (23) \\{P_{i}^{non} = \left\lbrack {{\sum\limits_{n = 0}^{z_{i}^{CS} - 1}\frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{n}}{n!}} + \frac{\left( {z_{i}^{CS}\rho_{i}^{RH}} \right)^{z_{i}^{CS}}}{{\left( z_{i}^{CS} \right)!}\left( {1 - \rho_{i}^{RH}} \right)}} \right\rbrack^{- 1}} & (24) \\{\rho_{i}^{RH} = \frac{\lambda_{i}^{RH}}{z_{i}^{CS}\mu}} & (25)\end{matrix}$ in the formulas: z_(i) ^(CS) is the number of chargingdevices configured for the node i, which is multiplied by p^(CS) toobtain a charge power of a single charging device at the node i; λ^(RH)is an average arrival rate of to-be-charged vehicles at the node iduring rush hours, i.e. the number of EVs arriving at the chargingstation to receive the charging service per unit of time; x_(k,i)^(road) denotes a binary variable of whether a flow on the path k can beintercepted by a charging station; Ω_(bd) is a set of shortest pathsfrom any starting point o to any ending point din the traffic network;W_(i) ^(RH) and W^(allowed) are an average waiting time for receiving acharging service during rush hours and a threshold thereof respectively;P_(i) ^(noon) is the probability that charging station devices at thenode i are all idle; ρ_(i) ^(PR) is an average device usage rate of thenode i during rush hours; N_(CS) is the maximum number of chargingstations to be constructed; and μ is an average service rate of a singledevice; the power grid constraints being as follows: power flowconstraints of the power distribution network: $\begin{matrix}\left\{ {{\begin{matrix}{{P_{s,i}^{L} + P_{s,i}^{CS} - P_{s,i}^{DG}} = {V_{s,i}{\sum\limits_{j = 1}^{n}{V_{s,j}\left( {{G_{ij}\cos \; \delta_{s,{ij}}} + {B_{ij}\sin \; \delta_{s,{ij}}}} \right)}}}} \\{{Q_{s,i}^{L} - Q_{s,i}^{DG}} = {V_{s,i}{\sum\limits_{j = 1}^{n}{V_{s,j}\left( {{G_{ij}\sin \; \delta_{s,{ij}}} - {B_{ij}\cos \; \delta_{s,{ij}}}} \right)}}}}\end{matrix}{\forall{s \in \Omega_{s}}}},{i \in \Omega}} \right. & (26)\end{matrix}$ scenario chance constraints: $\begin{matrix}{{{\Pr \left\{ {{V^{\min} \leq V_{s,i} \leq V^{\max}},{{P_{s,{ij}}} \leq P_{ij}^{\max}}} \right\}} = {\frac{K_{s}}{96} \geq {\gamma {\forall{i \in \Omega}}}}},{\forall{{ij} \in \Omega^{Line}}}} & (27)\end{matrix}$ DG mounting capacity constraints: $\begin{matrix}\left\{ \begin{matrix}{{0 \leq P_{s,j}^{PV} \leq {\overset{\_}{P}}_{s,j}^{PV}},{\forall{s \in \Omega_{s}}},{j \in \Omega^{PV}}} \\{{0 \leq P_{s,j}^{WG} \leq {\overset{\_}{P}}_{s,j}^{WG}},{\forall{s \in \Omega_{s}}},{j \in \Omega^{WG}}} \\{{\sum\limits_{s \in \Omega_{s}}\left( {P_{s,j}^{PV} + P_{s,j}^{WG}} \right)} \leq {ɛ{\sum\limits_{s \in \Omega_{s}}{\sum\limits_{i = 1}^{n}P_{s,i}^{L}}}}}\end{matrix} \right. & (28)\end{matrix}$ energy storage capacity and charge-discharge powerconstraints: $\begin{matrix}\left\{ {\begin{matrix}{{0 \leq S_{k}^{BS} \leq S_{\max}^{BS}},} \\{{0 \leq P_{k}^{BS} \leq P_{\max}^{BS}},}\end{matrix}{\forall{k \in \Omega^{BS}}}} \right. & (29)\end{matrix}$ in the formulas: Q_(s,i) ^(L) is a reactive load of thenode i in the scenario s; s_(s,i) ^(DG) and Q_(s,i) ^(DG) are DG activeand reactive outputs of the node i in the scenario s; V_(s,j) is avoltage amplitude of a node j in the scenario s; G_(ij) and B_(ij) arereal part and imaginary part of network admittances respectively;δ_(s,ij) is a voltage phase angle difference of the nodes i and j in thescenario s; P_(s,ij) and P_(ij) ^(max) are a power flowing through aline ij and a power limit; K_(s) is the number of scenarios meetingchance constraints; γ is a confidence coefficient; Ω^(Line) is a set ofpower distribution network lines; P _(s,j) ^(PV) and P _(s,j) ^(WG) areoutput upper limits of PV and WG respectively; ε is a maximumpenetration rate of DG access; and S_(k) ^(BS) and P_(k) ^(BS) are acurrent device capacity and a charge-discharge power of an energystorage node k respectively.